The implication of adjustable means that an event organizer (EO) can't fool all the audience all the time. If they tell the audience to come earlier than when they intend to start the event to counter people from being late, some newcomers like Gullible George may buy into it. However, Cynical Cindy may recognize the EO's intentions based on her previous experiences and her understanding of how those EOs conduct themselves and still come late. As a result, even though deceiving the people may work in the short run, their rational expectations will adjust and people will still end up being late.
The lesson is clear; to make sure that desired difference is close to zero in the long run, an EO must make sure that people perceive the events capable of delivering utility worth their time from minute 0. In the case of the general lecture, the EO must get the speaker to start on time even if the auditorium is only filled with one student. This must be painful for the organizers, but that is the price to establish credibility. In the long run, this should lead to people like Cynical Cindy to adjust their desired difference to zero, leading them to want to come on time.
On the way, lying in bed
In addition to participants' desired difference, they can even be tardier due to additional obstacles, represented in . Formally, is the difference in time on the first commencement of the event (i.e., when n = 1) caused by recurrent obstacles.
To understand this concept better, assume that Late Larry plans to come ten minutes late on her first day of college, making . However, as it is his first day, he hasn't figured out how long it might take for him to dress up, ride the public transport, and other routines did before arriving at college. If it turns out that doing those things caused him to be forty minutes late (=40), then his is 30 minutes.
Fortunately, although not in the case of Late Larry, can be a positive or negative constant; for example, a faster-than-usual commute can cause someone to come earlier than she desired. Regardless, it is this that creates a gap between the time an event starts and the time its participant wants to come in the first time.
However, Late Larry is not doomed to come 30 minutes later than when he desires to come as he can adapt and minimize the impact from these obstacles. As he goes to college more often, she starts to dress faster, learn the public transports' timetables, and optimize other routines so that they take less time. This concept is represented in , defined formally as how capable a person is in adapting and correcting the deviation from . In a sense, is a constant that incorporates both willpower and psychological characteristics, examples of which can be read here .
To illustrate the effect of how reduces the time difference between the actual time of arrival and ideal time of arrival, it is raised to the power of . As people only correct things after they have done something wrong, it is appropriate to use instead of just ; in the case of Late Lucy, her first adaptation towards is on her second day of college.
Since it is reasonable to assume that utility-maximizing people tend to try to be late by the amount of their desired difference, then should converge to 0 so that can converge to , as can be seen in Figure 3 below. In order for that to happen, should be a fraction between -1 and 1. It is important to note that it is possible for to be equal to -1 or 1, resulting in a uniform oscillating time path or a divergent line respectively. Regarding the concept of capability, the lower the absolute value of , the more capable the person is of adapting and overcoming the obstacles presented by as it allows for faster convergence.
People's absolute value of can also be lowered by helping them adapt faster to their regular obstacles. Programs such as orientation week, in which one helpful senior passes on information regarding the usual obstacles in coming on time, may help his juniors adapt faster and come on time, or at least on the time they aim to come.
